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Polytope of Type {6,24,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24,2}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157570)
Rank : 4
Schlafli Type : {6,24,2}
Number of vertices, edges, etc : 12, 144, 48, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,24,2}*576, {6,12,2}*576b
   3-fold quotients : {6,8,2}*384b
   4-fold quotients : {3,12,2}*288
   6-fold quotients : {3,8,2}*192, {6,4,2}*192
   8-fold quotients : {6,6,2}*144c
   12-fold quotients : {3,4,2}*96, {6,4,2}*96b, {6,4,2}*96c
   16-fold quotients : {3,6,2}*72
   24-fold quotients : {3,4,2}*48, {6,2,2}*48
   48-fold quotients : {3,2,2}*24
   72-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (  1,433)(  2,434)(  3,438)(  4,437)(  5,436)(  6,435)(  7,440)(  8,439)
(  9,449)( 10,450)( 11,454)( 12,453)( 13,452)( 14,451)( 15,456)( 16,455)
( 17,441)( 18,442)( 19,446)( 20,445)( 21,444)( 22,443)( 23,448)( 24,447)
( 25,481)( 26,482)( 27,486)( 28,485)( 29,484)( 30,483)( 31,488)( 32,487)
( 33,497)( 34,498)( 35,502)( 36,501)( 37,500)( 38,499)( 39,504)( 40,503)
( 41,489)( 42,490)( 43,494)( 44,493)( 45,492)( 46,491)( 47,496)( 48,495)
( 49,457)( 50,458)( 51,462)( 52,461)( 53,460)( 54,459)( 55,464)( 56,463)
( 57,473)( 58,474)( 59,478)( 60,477)( 61,476)( 62,475)( 63,480)( 64,479)
( 65,465)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,472)( 72,471)
( 73,505)( 74,506)( 75,510)( 76,509)( 77,508)( 78,507)( 79,512)( 80,511)
( 81,521)( 82,522)( 83,526)( 84,525)( 85,524)( 86,523)( 87,528)( 88,527)
( 89,513)( 90,514)( 91,518)( 92,517)( 93,516)( 94,515)( 95,520)( 96,519)
( 97,553)( 98,554)( 99,558)(100,557)(101,556)(102,555)(103,560)(104,559)
(105,569)(106,570)(107,574)(108,573)(109,572)(110,571)(111,576)(112,575)
(113,561)(114,562)(115,566)(116,565)(117,564)(118,563)(119,568)(120,567)
(121,529)(122,530)(123,534)(124,533)(125,532)(126,531)(127,536)(128,535)
(129,545)(130,546)(131,550)(132,549)(133,548)(134,547)(135,552)(136,551)
(137,537)(138,538)(139,542)(140,541)(141,540)(142,539)(143,544)(144,543)
(145,290)(146,289)(147,293)(148,294)(149,291)(150,292)(151,295)(152,296)
(153,306)(154,305)(155,309)(156,310)(157,307)(158,308)(159,311)(160,312)
(161,298)(162,297)(163,301)(164,302)(165,299)(166,300)(167,303)(168,304)
(169,338)(170,337)(171,341)(172,342)(173,339)(174,340)(175,343)(176,344)
(177,354)(178,353)(179,357)(180,358)(181,355)(182,356)(183,359)(184,360)
(185,346)(186,345)(187,349)(188,350)(189,347)(190,348)(191,351)(192,352)
(193,314)(194,313)(195,317)(196,318)(197,315)(198,316)(199,319)(200,320)
(201,330)(202,329)(203,333)(204,334)(205,331)(206,332)(207,335)(208,336)
(209,322)(210,321)(211,325)(212,326)(213,323)(214,324)(215,327)(216,328)
(217,362)(218,361)(219,365)(220,366)(221,363)(222,364)(223,367)(224,368)
(225,378)(226,377)(227,381)(228,382)(229,379)(230,380)(231,383)(232,384)
(233,370)(234,369)(235,373)(236,374)(237,371)(238,372)(239,375)(240,376)
(241,410)(242,409)(243,413)(244,414)(245,411)(246,412)(247,415)(248,416)
(249,426)(250,425)(251,429)(252,430)(253,427)(254,428)(255,431)(256,432)
(257,418)(258,417)(259,421)(260,422)(261,419)(262,420)(263,423)(264,424)
(265,386)(266,385)(267,389)(268,390)(269,387)(270,388)(271,391)(272,392)
(273,402)(274,401)(275,405)(276,406)(277,403)(278,404)(279,407)(280,408)
(281,394)(282,393)(283,397)(284,398)(285,395)(286,396)(287,399)(288,400);;
s1 := (  1,537)(  2,538)(  3,540)(  4,539)(  5,543)(  6,544)(  7,541)(  8,542)
(  9,529)( 10,530)( 11,532)( 12,531)( 13,535)( 14,536)( 15,533)( 16,534)
( 17,545)( 18,546)( 19,548)( 20,547)( 21,551)( 22,552)( 23,549)( 24,550)
( 25,513)( 26,514)( 27,516)( 28,515)( 29,519)( 30,520)( 31,517)( 32,518)
( 33,505)( 34,506)( 35,508)( 36,507)( 37,511)( 38,512)( 39,509)( 40,510)
( 41,521)( 42,522)( 43,524)( 44,523)( 45,527)( 46,528)( 47,525)( 48,526)
( 49,561)( 50,562)( 51,564)( 52,563)( 53,567)( 54,568)( 55,565)( 56,566)
( 57,553)( 58,554)( 59,556)( 60,555)( 61,559)( 62,560)( 63,557)( 64,558)
( 65,569)( 66,570)( 67,572)( 68,571)( 69,575)( 70,576)( 71,573)( 72,574)
( 73,465)( 74,466)( 75,468)( 76,467)( 77,471)( 78,472)( 79,469)( 80,470)
( 81,457)( 82,458)( 83,460)( 84,459)( 85,463)( 86,464)( 87,461)( 88,462)
( 89,473)( 90,474)( 91,476)( 92,475)( 93,479)( 94,480)( 95,477)( 96,478)
( 97,441)( 98,442)( 99,444)(100,443)(101,447)(102,448)(103,445)(104,446)
(105,433)(106,434)(107,436)(108,435)(109,439)(110,440)(111,437)(112,438)
(113,449)(114,450)(115,452)(116,451)(117,455)(118,456)(119,453)(120,454)
(121,489)(122,490)(123,492)(124,491)(125,495)(126,496)(127,493)(128,494)
(129,481)(130,482)(131,484)(132,483)(133,487)(134,488)(135,485)(136,486)
(137,497)(138,498)(139,500)(140,499)(141,503)(142,504)(143,501)(144,502)
(145,394)(146,393)(147,395)(148,396)(149,400)(150,399)(151,398)(152,397)
(153,386)(154,385)(155,387)(156,388)(157,392)(158,391)(159,390)(160,389)
(161,402)(162,401)(163,403)(164,404)(165,408)(166,407)(167,406)(168,405)
(169,370)(170,369)(171,371)(172,372)(173,376)(174,375)(175,374)(176,373)
(177,362)(178,361)(179,363)(180,364)(181,368)(182,367)(183,366)(184,365)
(185,378)(186,377)(187,379)(188,380)(189,384)(190,383)(191,382)(192,381)
(193,418)(194,417)(195,419)(196,420)(197,424)(198,423)(199,422)(200,421)
(201,410)(202,409)(203,411)(204,412)(205,416)(206,415)(207,414)(208,413)
(209,426)(210,425)(211,427)(212,428)(213,432)(214,431)(215,430)(216,429)
(217,322)(218,321)(219,323)(220,324)(221,328)(222,327)(223,326)(224,325)
(225,314)(226,313)(227,315)(228,316)(229,320)(230,319)(231,318)(232,317)
(233,330)(234,329)(235,331)(236,332)(237,336)(238,335)(239,334)(240,333)
(241,298)(242,297)(243,299)(244,300)(245,304)(246,303)(247,302)(248,301)
(249,290)(250,289)(251,291)(252,292)(253,296)(254,295)(255,294)(256,293)
(257,306)(258,305)(259,307)(260,308)(261,312)(262,311)(263,310)(264,309)
(265,346)(266,345)(267,347)(268,348)(269,352)(270,351)(271,350)(272,349)
(273,338)(274,337)(275,339)(276,340)(277,344)(278,343)(279,342)(280,341)
(281,354)(282,353)(283,355)(284,356)(285,360)(286,359)(287,358)(288,357);;
s2 := (  1,295)(  2,296)(  3,293)(  4,294)(  5,292)(  6,291)(  7,290)(  8,289)
(  9,311)( 10,312)( 11,309)( 12,310)( 13,308)( 14,307)( 15,306)( 16,305)
( 17,303)( 18,304)( 19,301)( 20,302)( 21,300)( 22,299)( 23,298)( 24,297)
( 25,319)( 26,320)( 27,317)( 28,318)( 29,316)( 30,315)( 31,314)( 32,313)
( 33,335)( 34,336)( 35,333)( 36,334)( 37,332)( 38,331)( 39,330)( 40,329)
( 41,327)( 42,328)( 43,325)( 44,326)( 45,324)( 46,323)( 47,322)( 48,321)
( 49,343)( 50,344)( 51,341)( 52,342)( 53,340)( 54,339)( 55,338)( 56,337)
( 57,359)( 58,360)( 59,357)( 60,358)( 61,356)( 62,355)( 63,354)( 64,353)
( 65,351)( 66,352)( 67,349)( 68,350)( 69,348)( 70,347)( 71,346)( 72,345)
( 73,367)( 74,368)( 75,365)( 76,366)( 77,364)( 78,363)( 79,362)( 80,361)
( 81,383)( 82,384)( 83,381)( 84,382)( 85,380)( 86,379)( 87,378)( 88,377)
( 89,375)( 90,376)( 91,373)( 92,374)( 93,372)( 94,371)( 95,370)( 96,369)
( 97,391)( 98,392)( 99,389)(100,390)(101,388)(102,387)(103,386)(104,385)
(105,407)(106,408)(107,405)(108,406)(109,404)(110,403)(111,402)(112,401)
(113,399)(114,400)(115,397)(116,398)(117,396)(118,395)(119,394)(120,393)
(121,415)(122,416)(123,413)(124,414)(125,412)(126,411)(127,410)(128,409)
(129,431)(130,432)(131,429)(132,430)(133,428)(134,427)(135,426)(136,425)
(137,423)(138,424)(139,421)(140,422)(141,420)(142,419)(143,418)(144,417)
(145,440)(146,439)(147,438)(148,437)(149,435)(150,436)(151,433)(152,434)
(153,456)(154,455)(155,454)(156,453)(157,451)(158,452)(159,449)(160,450)
(161,448)(162,447)(163,446)(164,445)(165,443)(166,444)(167,441)(168,442)
(169,464)(170,463)(171,462)(172,461)(173,459)(174,460)(175,457)(176,458)
(177,480)(178,479)(179,478)(180,477)(181,475)(182,476)(183,473)(184,474)
(185,472)(186,471)(187,470)(188,469)(189,467)(190,468)(191,465)(192,466)
(193,488)(194,487)(195,486)(196,485)(197,483)(198,484)(199,481)(200,482)
(201,504)(202,503)(203,502)(204,501)(205,499)(206,500)(207,497)(208,498)
(209,496)(210,495)(211,494)(212,493)(213,491)(214,492)(215,489)(216,490)
(217,512)(218,511)(219,510)(220,509)(221,507)(222,508)(223,505)(224,506)
(225,528)(226,527)(227,526)(228,525)(229,523)(230,524)(231,521)(232,522)
(233,520)(234,519)(235,518)(236,517)(237,515)(238,516)(239,513)(240,514)
(241,536)(242,535)(243,534)(244,533)(245,531)(246,532)(247,529)(248,530)
(249,552)(250,551)(251,550)(252,549)(253,547)(254,548)(255,545)(256,546)
(257,544)(258,543)(259,542)(260,541)(261,539)(262,540)(263,537)(264,538)
(265,560)(266,559)(267,558)(268,557)(269,555)(270,556)(271,553)(272,554)
(273,576)(274,575)(275,574)(276,573)(277,571)(278,572)(279,569)(280,570)
(281,568)(282,567)(283,566)(284,565)(285,563)(286,564)(287,561)(288,562);;
s3 := (577,578);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(578)!(  1,433)(  2,434)(  3,438)(  4,437)(  5,436)(  6,435)(  7,440)
(  8,439)(  9,449)( 10,450)( 11,454)( 12,453)( 13,452)( 14,451)( 15,456)
( 16,455)( 17,441)( 18,442)( 19,446)( 20,445)( 21,444)( 22,443)( 23,448)
( 24,447)( 25,481)( 26,482)( 27,486)( 28,485)( 29,484)( 30,483)( 31,488)
( 32,487)( 33,497)( 34,498)( 35,502)( 36,501)( 37,500)( 38,499)( 39,504)
( 40,503)( 41,489)( 42,490)( 43,494)( 44,493)( 45,492)( 46,491)( 47,496)
( 48,495)( 49,457)( 50,458)( 51,462)( 52,461)( 53,460)( 54,459)( 55,464)
( 56,463)( 57,473)( 58,474)( 59,478)( 60,477)( 61,476)( 62,475)( 63,480)
( 64,479)( 65,465)( 66,466)( 67,470)( 68,469)( 69,468)( 70,467)( 71,472)
( 72,471)( 73,505)( 74,506)( 75,510)( 76,509)( 77,508)( 78,507)( 79,512)
( 80,511)( 81,521)( 82,522)( 83,526)( 84,525)( 85,524)( 86,523)( 87,528)
( 88,527)( 89,513)( 90,514)( 91,518)( 92,517)( 93,516)( 94,515)( 95,520)
( 96,519)( 97,553)( 98,554)( 99,558)(100,557)(101,556)(102,555)(103,560)
(104,559)(105,569)(106,570)(107,574)(108,573)(109,572)(110,571)(111,576)
(112,575)(113,561)(114,562)(115,566)(116,565)(117,564)(118,563)(119,568)
(120,567)(121,529)(122,530)(123,534)(124,533)(125,532)(126,531)(127,536)
(128,535)(129,545)(130,546)(131,550)(132,549)(133,548)(134,547)(135,552)
(136,551)(137,537)(138,538)(139,542)(140,541)(141,540)(142,539)(143,544)
(144,543)(145,290)(146,289)(147,293)(148,294)(149,291)(150,292)(151,295)
(152,296)(153,306)(154,305)(155,309)(156,310)(157,307)(158,308)(159,311)
(160,312)(161,298)(162,297)(163,301)(164,302)(165,299)(166,300)(167,303)
(168,304)(169,338)(170,337)(171,341)(172,342)(173,339)(174,340)(175,343)
(176,344)(177,354)(178,353)(179,357)(180,358)(181,355)(182,356)(183,359)
(184,360)(185,346)(186,345)(187,349)(188,350)(189,347)(190,348)(191,351)
(192,352)(193,314)(194,313)(195,317)(196,318)(197,315)(198,316)(199,319)
(200,320)(201,330)(202,329)(203,333)(204,334)(205,331)(206,332)(207,335)
(208,336)(209,322)(210,321)(211,325)(212,326)(213,323)(214,324)(215,327)
(216,328)(217,362)(218,361)(219,365)(220,366)(221,363)(222,364)(223,367)
(224,368)(225,378)(226,377)(227,381)(228,382)(229,379)(230,380)(231,383)
(232,384)(233,370)(234,369)(235,373)(236,374)(237,371)(238,372)(239,375)
(240,376)(241,410)(242,409)(243,413)(244,414)(245,411)(246,412)(247,415)
(248,416)(249,426)(250,425)(251,429)(252,430)(253,427)(254,428)(255,431)
(256,432)(257,418)(258,417)(259,421)(260,422)(261,419)(262,420)(263,423)
(264,424)(265,386)(266,385)(267,389)(268,390)(269,387)(270,388)(271,391)
(272,392)(273,402)(274,401)(275,405)(276,406)(277,403)(278,404)(279,407)
(280,408)(281,394)(282,393)(283,397)(284,398)(285,395)(286,396)(287,399)
(288,400);
s1 := Sym(578)!(  1,537)(  2,538)(  3,540)(  4,539)(  5,543)(  6,544)(  7,541)
(  8,542)(  9,529)( 10,530)( 11,532)( 12,531)( 13,535)( 14,536)( 15,533)
( 16,534)( 17,545)( 18,546)( 19,548)( 20,547)( 21,551)( 22,552)( 23,549)
( 24,550)( 25,513)( 26,514)( 27,516)( 28,515)( 29,519)( 30,520)( 31,517)
( 32,518)( 33,505)( 34,506)( 35,508)( 36,507)( 37,511)( 38,512)( 39,509)
( 40,510)( 41,521)( 42,522)( 43,524)( 44,523)( 45,527)( 46,528)( 47,525)
( 48,526)( 49,561)( 50,562)( 51,564)( 52,563)( 53,567)( 54,568)( 55,565)
( 56,566)( 57,553)( 58,554)( 59,556)( 60,555)( 61,559)( 62,560)( 63,557)
( 64,558)( 65,569)( 66,570)( 67,572)( 68,571)( 69,575)( 70,576)( 71,573)
( 72,574)( 73,465)( 74,466)( 75,468)( 76,467)( 77,471)( 78,472)( 79,469)
( 80,470)( 81,457)( 82,458)( 83,460)( 84,459)( 85,463)( 86,464)( 87,461)
( 88,462)( 89,473)( 90,474)( 91,476)( 92,475)( 93,479)( 94,480)( 95,477)
( 96,478)( 97,441)( 98,442)( 99,444)(100,443)(101,447)(102,448)(103,445)
(104,446)(105,433)(106,434)(107,436)(108,435)(109,439)(110,440)(111,437)
(112,438)(113,449)(114,450)(115,452)(116,451)(117,455)(118,456)(119,453)
(120,454)(121,489)(122,490)(123,492)(124,491)(125,495)(126,496)(127,493)
(128,494)(129,481)(130,482)(131,484)(132,483)(133,487)(134,488)(135,485)
(136,486)(137,497)(138,498)(139,500)(140,499)(141,503)(142,504)(143,501)
(144,502)(145,394)(146,393)(147,395)(148,396)(149,400)(150,399)(151,398)
(152,397)(153,386)(154,385)(155,387)(156,388)(157,392)(158,391)(159,390)
(160,389)(161,402)(162,401)(163,403)(164,404)(165,408)(166,407)(167,406)
(168,405)(169,370)(170,369)(171,371)(172,372)(173,376)(174,375)(175,374)
(176,373)(177,362)(178,361)(179,363)(180,364)(181,368)(182,367)(183,366)
(184,365)(185,378)(186,377)(187,379)(188,380)(189,384)(190,383)(191,382)
(192,381)(193,418)(194,417)(195,419)(196,420)(197,424)(198,423)(199,422)
(200,421)(201,410)(202,409)(203,411)(204,412)(205,416)(206,415)(207,414)
(208,413)(209,426)(210,425)(211,427)(212,428)(213,432)(214,431)(215,430)
(216,429)(217,322)(218,321)(219,323)(220,324)(221,328)(222,327)(223,326)
(224,325)(225,314)(226,313)(227,315)(228,316)(229,320)(230,319)(231,318)
(232,317)(233,330)(234,329)(235,331)(236,332)(237,336)(238,335)(239,334)
(240,333)(241,298)(242,297)(243,299)(244,300)(245,304)(246,303)(247,302)
(248,301)(249,290)(250,289)(251,291)(252,292)(253,296)(254,295)(255,294)
(256,293)(257,306)(258,305)(259,307)(260,308)(261,312)(262,311)(263,310)
(264,309)(265,346)(266,345)(267,347)(268,348)(269,352)(270,351)(271,350)
(272,349)(273,338)(274,337)(275,339)(276,340)(277,344)(278,343)(279,342)
(280,341)(281,354)(282,353)(283,355)(284,356)(285,360)(286,359)(287,358)
(288,357);
s2 := Sym(578)!(  1,295)(  2,296)(  3,293)(  4,294)(  5,292)(  6,291)(  7,290)
(  8,289)(  9,311)( 10,312)( 11,309)( 12,310)( 13,308)( 14,307)( 15,306)
( 16,305)( 17,303)( 18,304)( 19,301)( 20,302)( 21,300)( 22,299)( 23,298)
( 24,297)( 25,319)( 26,320)( 27,317)( 28,318)( 29,316)( 30,315)( 31,314)
( 32,313)( 33,335)( 34,336)( 35,333)( 36,334)( 37,332)( 38,331)( 39,330)
( 40,329)( 41,327)( 42,328)( 43,325)( 44,326)( 45,324)( 46,323)( 47,322)
( 48,321)( 49,343)( 50,344)( 51,341)( 52,342)( 53,340)( 54,339)( 55,338)
( 56,337)( 57,359)( 58,360)( 59,357)( 60,358)( 61,356)( 62,355)( 63,354)
( 64,353)( 65,351)( 66,352)( 67,349)( 68,350)( 69,348)( 70,347)( 71,346)
( 72,345)( 73,367)( 74,368)( 75,365)( 76,366)( 77,364)( 78,363)( 79,362)
( 80,361)( 81,383)( 82,384)( 83,381)( 84,382)( 85,380)( 86,379)( 87,378)
( 88,377)( 89,375)( 90,376)( 91,373)( 92,374)( 93,372)( 94,371)( 95,370)
( 96,369)( 97,391)( 98,392)( 99,389)(100,390)(101,388)(102,387)(103,386)
(104,385)(105,407)(106,408)(107,405)(108,406)(109,404)(110,403)(111,402)
(112,401)(113,399)(114,400)(115,397)(116,398)(117,396)(118,395)(119,394)
(120,393)(121,415)(122,416)(123,413)(124,414)(125,412)(126,411)(127,410)
(128,409)(129,431)(130,432)(131,429)(132,430)(133,428)(134,427)(135,426)
(136,425)(137,423)(138,424)(139,421)(140,422)(141,420)(142,419)(143,418)
(144,417)(145,440)(146,439)(147,438)(148,437)(149,435)(150,436)(151,433)
(152,434)(153,456)(154,455)(155,454)(156,453)(157,451)(158,452)(159,449)
(160,450)(161,448)(162,447)(163,446)(164,445)(165,443)(166,444)(167,441)
(168,442)(169,464)(170,463)(171,462)(172,461)(173,459)(174,460)(175,457)
(176,458)(177,480)(178,479)(179,478)(180,477)(181,475)(182,476)(183,473)
(184,474)(185,472)(186,471)(187,470)(188,469)(189,467)(190,468)(191,465)
(192,466)(193,488)(194,487)(195,486)(196,485)(197,483)(198,484)(199,481)
(200,482)(201,504)(202,503)(203,502)(204,501)(205,499)(206,500)(207,497)
(208,498)(209,496)(210,495)(211,494)(212,493)(213,491)(214,492)(215,489)
(216,490)(217,512)(218,511)(219,510)(220,509)(221,507)(222,508)(223,505)
(224,506)(225,528)(226,527)(227,526)(228,525)(229,523)(230,524)(231,521)
(232,522)(233,520)(234,519)(235,518)(236,517)(237,515)(238,516)(239,513)
(240,514)(241,536)(242,535)(243,534)(244,533)(245,531)(246,532)(247,529)
(248,530)(249,552)(250,551)(251,550)(252,549)(253,547)(254,548)(255,545)
(256,546)(257,544)(258,543)(259,542)(260,541)(261,539)(262,540)(263,537)
(264,538)(265,560)(266,559)(267,558)(268,557)(269,555)(270,556)(271,553)
(272,554)(273,576)(274,575)(275,574)(276,573)(277,571)(278,572)(279,569)
(280,570)(281,568)(282,567)(283,566)(284,565)(285,563)(286,564)(287,561)
(288,562);
s3 := Sym(578)!(577,578);
poly := sub<Sym(578)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1 >; 
 

to this polytope